Device for generating arcs or the like



June 17, 1952 E. H. WANG 2,600,591

DEVICE FOR GENERATING ARCS OR THE LIKE Filed March 17, 1949 INVENTOR.[If/6 M "4 1%",

ATTORNEY-S- Patented June 17, 1952 DEVICE FOR GENERATING ARCS on THELIKE Eric H. Wang, Cincinnati, Ohio Application March 17, 1949, SerialNo. 81,993

3 Claims.

My invention relates toqa device and process for generating arcs of aradius which is so large that it is impossible or impractical to usethecenter of the arc as a pivot point.

In machining, engraving, and other purposes, it is often desirable togenerate an arc with the tool wherein the chord or length of the arc isrelatively short, but the radius of the arc extremely large, but wherethe center of the arc is so remote from the machine or engravingapparatus that it is impossible or impractical to use the center as apivot about which to revolve an arm.

It is an object of my invention to provide a device for generating arcsof large radius to an accuracy sufficient for practical purposes whichis located substantially on the are being generated and without thenecessity of any portion of the device projecting to or being connectedto any center remote from the device.

It is a further object of my invention to provide a process and devicefor simply and readily generating arcs of sufficient accuracy forpractical purposes which is quite simple to construct and maintain andwhich may be easily altered to generate arcs of different radii anddifferent lengths.

While in the following drawings and description I will show and describea device primarily for use with a planer or a milling machine, it is tobe understood that this is merely exemplary of my process and devicesince the process and device may be used for many other purposes such asengraving, drawing, or any place where it is desirable to generate anarc of relatively large radius for practical and non-mathematicalpurposes.

These and other objects of my invention which will be set forthhereinafter or will be apparent to one skilled in the art upon readingthese specifications, I accomplish by that certain construction andarrangement of parts of which I shall now describe an exemplaryembodiment. Reference is made to the drawings in which:

Figure l is a sketch showing a near approximation to a circular aregenerated by the tool of my device and a true circular arc of very largeradius.

Figure 2 shows the movement of the work piece in reference to the toolwhereby the arc is generated.

Figure 3 shows my device as applied to the table and bed of a planer inplane.

Figure 4 shows my device as applied to the table and bed of a planer inelevation.

Figure 5 shows my device as applied to a milling machine in elevation.

Briefly, in the practice of my invention, I have determined that aportion of the loop of a looped trochoid in its special case, anarchimedic spiral,

' very closely approaches the true are of a circle of substantial radiusin referring to a relatively short chord or are. I have determined thata trochoid can, for example, be generated by translating the work piecein a straight line, while at the same time rotating it through a certainrather small angle and that any tool which is stationary as to itsposition on the machine will describe in the work piece a part of thetrochoidal curve.

The distance to be traveled and the angle through which the work piecemust rotate while traveling this distance will be in a constant ratiofor each case and will depend on (a) the distance of the lowest point ofthe trochoid to the center of rotation of the work piece. This is equalto the distance of the points of contact of the tool to the straightline which the center 'of rotation of the 'work piece describes. (b) Theradius desired, and (c) the length of the chord between the end pointsof the are desired.

The calculation is based on a trochoid which coincides in three pointswith the desired are, preferably a point at or near each end of thedesired circular arc and an intermediate point. Computations actuallyperformed show a deviation of only a few thousandthsof an inch down toless than one thousandth of an inch at the place where the trochoidwhich is generated and the circular are which is desired are furthestapart.

The deviation between the trochoid generated and the circular aredesired becomes smaller with increasing radius and relativelydiminishing chord. For an arc of 240 inch radius and a chord of incheslength, the deviation is less than .001 inch.

Figure 1 shows a piece of work I into which a circular arc 2 is to becut. Points A and C as well as intermediate B are identical with the are2 and the trochoid 3 which is generated and indicated by the brokenline. The point of greatest deviation between the trochoid 3 and the are2 is at 4 and as heretofore pointed out is extremely small, and forpractical purposes is negligible, diminishing as the radius increases.

The equation of the trochoid can be developed by using the equation ofthe involute to start known and may be determined for each individualsetting based on the radius of the arc to be cut or generated and thelength of the chord.

In Figure 2, the starting position of the work piece I is shown at 5 andthe end position of the work piece I is shown at 6. The position of thetool which is stationary is shown at I. The rotating work holder isindicated at 8 and in Figure 2 rotates in a clockwise direction aboutthe center 9 and the distance the tool holder 8'is'translated is-thedistance between the centers 9-9 in Figure 2. The broken line 10indicates the arc (trochoid generated) to be cut by the tool I and isshown completed at ID in Figure 2.

Figures 3 and 4 show my device as applied to a planer having areciprocating or translating table II and a stationary bed 12. Therotating work holder 8 is positioned on the table II and reciprocateswith it. The work I is held in position by suitable clamps 13. The tool14 is held by the normal tool holder [5.

A gear'l6 mounted on a shaft ll whichrotates the work holder 8 about itscenterBby means of mechanismnot showniscommon in the art. A train ofgears-lawns from the .gear [6 tea rack l9 which is mounted by means oibrackets 29 to the bed l2.

From the above, it is apparent that by selecting gears of specificrelative sizes for thegear train|8 the ratio of translation to rotationof the work I may be adjusted so that the tool M will generate a portionof a specific trochoid 10 in the work I.

Figurefi shows the application of my device to a milling machine havingreciprocating or translating table and a stationary base 2!. Theleadscrew of the milling machine-22 is connected by gearing 18 to theshaft H which rotates the work holding table 8. The milling cutter 23rotatestc cut the material but-does not move ina horizontal plane. Theaction :is the same as that described in reference to the planer, thatis, the'ratio of the translation of the table 2| to the rotation of .thework holding table 8 is covered by the gears 18 and is soadjusted thatthe tool 23'will generate the desired portion ofthe specific trochoid onthe work I.

While I have described my invention. as applied to a planer or a millingmachine, itis tobe understood that I do not intend to limit myselfspecifically to these two machines since the application isadaptable tonumerous other machine tools as'well asengraving machines and otherdevices Where it is desirable to have a tool or stylus generate aportion of a trochoid or similar figure.

As is apparent, the device is relatively simple, rugged, and subject tocomplete control.

It is to be understood that modification may be made in my inventionwithout departing from the spirit thereof. Having thus described myinvention in an exemplary embodiment, what I claim as new and desire tosecure by Letters Patent is:

1. In a planer or the like a rotatable work holder positioned on thereciprocating table of the planer with its axis of rotationperpendicular to the direction of reciprocation of the table, a rackassociated with the stationary planer bed, a train of gears engaging therack and the work holder for rotation thereof in fixed relation to thetranslation of the table and a stationary tool positioned over the workholder.

2. In a planer or the like a rotatable work holder positioned on thereciprocating table of the planer with its axis of rotationperpendicular to the direction of reciprocation of the table, a rackassociated with the stationary planer bed, a train of gears'engaging therackv and the work holder for rotation thereof in fixed relation to thetranslation of the table and a stationary tool positioned over the workholder, said train of gears being variable.

3. In a machine tool or the like, a stationary bed, a rack fixed on thebed, a reciprocating table on the bed, a rotatable Work holder on saidtable having its axis of rotation perpendicular to the direction ofreciprocation of the table, a single series of intermeshing gears, saidgears being interconnected with the rotary work holder, thereciprocating table and the stationary rack. whereby said work holder isrotatable and the table reciprocable simultaneously.

ERIC H. WANG.

REFERENCES CITED The following references are of record in the file ofthis patent:

UNITED STATES PATENTS Number Name Date 1,355,919 Schurr Oct. 19, 19201,835,742 Andrew Dec. 8, 1931 1,901,952 Emerson Mar. 21, 1933 2,303,813Barcus Dec. 1, 1942 2,330,921 Rickenmann Oct. 5, 1943 2,350,428 TormaJan. 6, 1944 2,366,993 Antos Jan/9, 1945

